Embedding separable spaces $\mathcal{C}(L)$ in arbitrary spaces $\mathcal{C}(K)$
| Autor: | Rondoš, Jakub, Sobota, Damian |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | For a compact metric space $L$ and a compact space $K$, and their Banach spaces $\mathcal{C}(L)$ and $\mathcal{C}(K)$ of continuous functions, we provide several characterizations of the presence of isometric, resp. isomorphic, copies of $\mathcal{C}(L)$ in $\mathcal{C}(K)$, in particular, in terms of Cantor--Bendixson derivatives of $L$ and $K$. We also describe the relative cellularities of the perfect kernel of $K$ and of Cantor--Bendixson derived sets of $K$ of countable order in terms of the existence of isometric copies of specific spaces $\mathcal{C}(L)$ inside $\mathcal{C}(K)$. Comment: 21 pages |
| Databáze: | arXiv |
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